Download Algebra II - District 303

MATH - Algebra II
CUSD 303
Year 2012-2013
Content
Cluster Standard
The Complex
Perform arithmetic
Number System operations with complex
numbers
Use complex numbers in
polynomial identities and
equations
The Real
Extend the properties of
Number System exponents to rational
exponents
Seeing Structure Interpret the structure of
in Expressions expression
Write expressions in
equivalent forms to solve
problems
Standard
A2.NCN1 Know there is a complex number i such that i2 = −1, and
every complex number has the form a + bi with a and b real
Skill Statements
A2.NCN1 Recognize there is a complex number
A2.NCN1 Recognize every complex number as the form a + bi with
a and b as real numbers
A2.NCN2 Use the relation i2 = –1 and the commutative, associative, A2.NCN2 Add complex numbers using the relation i2 = -1 and the
and distributive properties to add, subtract, and multiply complex
commutative, associative, and distributive properties
numbers
A2.NCN2 Subtract complex numbers using the relation i2 = -1 and
the commutative, associative, and distributive properties
A2.NCN7 Solve quadratic equations with real coefficients that have
complex solutions
A2.NCN8 (+) Extend polynomial identities to the complex numbers
For example, rewrite x2 + 4 as (x + 2i)(x – 2i)
A2.NCN9 (+) Know the Fundamental Theorem of Algebra; show that
it is true for quadratic polynomials
A.NRN1 Explain how the definition of the meaning of rational
exponents follows from extending the properties of integer
exponents to those values, allowing for a notation for radicals in
terms of rational exponents For example, we define 51/3 to be the
cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3
must equal 5
A.NRN2 Rewrite expressions involving radicals and rational
exponents using the properties of exponents
A.ASSE1 Interpret expressions that represent a quantity in terms of
its context
A.ASSE1a Interpret parts of an expression, such as terms, factors,
and coefficients
A2.ASSE1b Interpret complicated expressions by viewing one or
more of their parts as a single entity For example, interpret P(1+r)n
as the product of P and a factor not depending on P
A2.ASSE2 Use the structure of an expression to identify ways to
rewrite it For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing
it as a difference of squares that can be factored as (x2 – y2)(x2 +
y2)**
A2.ASSE4 Derive the formula for the sum of a finite geometric
series (when the common ratio is not 1), and use the formula to
solve problems For example, calculate mortgage payments
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A2.NCN2 Multiply complex numbers using the relation i 2 = -1 and
the commutative, associative, and distributive properties
A2.NCN7 Solve quadratic equations with real coefficients that have
complex solutions
A2.NCN8 (+) Extend polynomial identities to the complex numbers
A2.NCN9 (+) Provide evidence that the Fundamental Theorem of
Algebra is true for quadratic polynomials
T3.A.NRN1 Explain how the definition of the meaning of rational
exponents follows from extending the properties of integer
exponents to those values, allowing for a notation for radicals in
terms of rational exponents
T3.A.NRN2 Rewrite expressions involving radicals as rational
exponents using the properties of exponents
T3.A.NRN2 Rewrite expressions involving rational exponents as
radicals using the properties of exponents
A2.ASSE1 Interpret expressions that represent a quantity in terms of
its context
A2.ASSE1a Interpret parts of an expression
A2.ASSE1b Interpret complicated expressions by viewing one or
more of their parts as a single entity
T3.A2.ASSE2 Extend knowledge of factoring patterns to more
complex cases
A2.ASSE2 Recognize the structure of an expression and identify
ways in order to rewrite the expression in equivalent forms
A2.ASSE4 Derive the formula for the sum of a finite geometric
series (when the common ratio is not 1)
A2.ASSE4 Solve problems using the formula for the sum of a finite
geometric series
A2.ASSE4 (+)Derive the formula for the sum of a infinite geometric
series (when the common ratio is not 1)
A2.ASSE4 (+) Solve problems using the formula for the sum of a
infinite geometric series
Resources
Core
Connections
Algebra 2, 2012,
College
Preparatory
Mathematics
(CPM)
Content
Cluster Standard
Arithmetic with Perform arithmetic
Polynomials and operations on polynomials
Rational
Expressions
Standard
A2.AAPR1 Understand that polynomials form a system analogous to
the integers, namely, they are closed under the operations of
addition, subtraction, and multiplication; add, subtract, and multiply
polynomials
Skill Statements
T3.A2.AAPR1 Define a closed system in relation to integers to
extend to their knowledge of polynomials
A2.AAPR1 Recognize that polynomials form a system analogous to
the integers, namely, they are closed under the operations of
addition, subtraction, and multiplication but not division
A2.AAPR1 Add polynomials
A2.AAPR1 Subtract polynomials
A2.AAPR1 Multiply polynomials
Understand the relationship A2.AAPR2 Know and apply the Remainder Theorem: For a
T3.A2.AAPR2 Apply long division to polynomials
between zeros and factors polynomial p(x) and a number a, the remainder on division by x – a A2.AAPR2 Apply the Remainder Theorem: For a polynomial p(x)
of polynomials
is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x)
and a number a, the remainder on division by x – a is p(a), so p(a) =
0 if and only if (x – a) is a factor of p(x)
A2.AAPR3 Identify zeros of polynomials when suitable factorizations A2.AAPR3 Identify zeros of polynomials when suitable factorizations
are available, and use the zeros to construct a rough graph of the
are available
function defined by the polynomial
A2.AAPR3 Construct a rough graph of the function defined by the
polynomial using its zeros
Use polynomial identities to A2.AAPR4 Prove polynomial identities and use them to describe
A2.AAPR4 Prove polynomial identities
solve problems
numerical relationships For example, the polynomial identity (x2 +
A2.AAPR4 Describe the numerical relationships between the
y2)2 = (x2 – y2)2 + (2xy)2 can be used to generate Pythagorean
expanded and condensed forms of the polynomial identities???
triples
A2.AAPR5 (+) Know and apply the Binomial Theorem for the
A2.AAPR5 (+) Apply the Binomial Theorem for the expansion of (x +
expansion of (x + y)n in powers of x and y for a positive integer n,
y)n in powers of x and y for a positive integer n, where x and y are
where x and y are any numbers, with coefficients determined for
any numbers, with coefficients determined for example by Pascal’s
example by Pascal’s Triangle
Triangle
Rewrite rational expressions A2.AAPR6 Rewrite simple rational expressions in different forms;
write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and
r(x) are polynomials with the degree of r(x) less than the degree of
b(x), using inspection, long division, or, for the more complicated
examples, a computer algebra system
A2.AAPR7 (+) Understand that rational expressions form a system
analogous to the rational numbers, closed under addition,
subtraction, multiplication, and division by a nonzero rational
expression; add, subtract, multiply, and divide rational expressions
Creating
Equations
Create equations that
describe numbers or
relationships
T3.A2.AAPR6 Apply long division to polynomials
A2.AAPR6 Divide two polynomials and correctly express the
remainder, if it exists
A2.AAPR7 (+) Recognize that rational expressions form a system
analogous to the rational numbers, namely, they are closed under
the operations of addition, subtraction multiplication and division
A2.AAPR7 (+) Add rational expressions
A2.AAPR7 (+) Subtract rational expressions
A2.AAPR7 (+) Multiply rational expressions
A2.AAPR7 (+) Divide rational expressions
A.ACED1 Create equations and inequalities in one variable and use T3.A.ACED1 Create exponential equations with integer exponents in
them to solve problems. Include equations arising from linear and
one variable
quadratic functions, and simple rational and exponential functions
T3.A.ACED1 Evaluate exponential equations with integer exponents
in one variable
T3.A.ACED1 Create exponential inequalities with integer exponents
in one variable
T3.A.ACED1 Evaluate exponential inequalities with integer
exponents in one variable
T3.A2.ACED1 Define the properties of equations: (3) Simple
Rational (4) Simple Exponential (5) Simple Root
A2.ACED1 Create equations in one variable arising from the
following functions: (1) Linear, (2) Quadratic, (3) Simple Rational (4)
Simple Exponential (5) Simple Root
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Resources
Core
Connections
Algebra 2, 2012,
College
Preparatory
Mathematics
(CPM)
Content
Creating
Equations
(cont'd)
Cluster Standard
Create equations that
describe numbers or
relationships (cont'd)
Standard
A.ACED2 Create equations in two or more variables to represent
relationships between quantities; graph equations on coordinate
axes with labels and scales
Skill Statements
A2.ACED1 Solve problems using equations in one variable arising
from the following functions: (1) Linear, (2) Quadratic, (3) Simple
Rational (4) Simple Exponential (5) Simple Root
A2.ACED1 Create inequalities in one variable arising from the
following functions: (1) Linear, (2) Quadratic, (3) Simple Rational (4)
Simple Exponential (5) Simple Root
A2.ACED1 Solve problems using equations in one variable arising
from the following functions: (1) Linear, (2) Quadratic, (3) Simple
Rational (4) Simple Exponential (5) Simple Root
T3.A.ACED2 Create exponential equations with integer exponents in
two variables to represent relationships between quantities
T3.A.ACED2 Graph exponential equations with integer exponents
on coordinate axes with labels and scales
A2.ACED2 Create equations in two or more variables to represent
relationships between quantities. The equations created will
represent (but are not limited to) linear, quadratic and exponential
relationships
A2.ACED3 Represent constraints by equations or inequalities, and
by systems of equations and/or inequalities, and interpret solutions
as viable or non-viable options in a modeling context. For example,
represent inequalities describing nutritional and cost constraints on
combinations of different foods
A2.ACED4 Rearrange formulas to highlight a quantity of interest,
using the same reasoning as in solving equations For example,
rearrange Ohm’s law V = IR to highlight resistance R
Reasoning with
Equations and
Inequalities
Understand solving
equations as a process of
reasoning and explain the
reasoning
Solve equations and
inequalities in one variable
Represent and solve
equations and inequalities
graphically
A2.ACED2 Graph equations on coordinate axes (x,y) with labels and
scales. The equations graphed will represent (but are not limited to)
linear, quadratic and exponential relationships
A2.ACED3 Represent constraints by equations or inequalities, and
by systems of equations and/or inequalities
A2.ACED3 Interpret solutions as viable or non-viable options in a
modeling context
T3.A2.ACED4 Apply the order of operations to solve for given
variables when there are two or more variables in a function
A2.ACED4 Manipulate literal equations to solve for a given variable
A2.AREI2 Solve simple rational and radical equations in one
A2.AREI2 Solve simple rational equations in one variable
variable, and give examples showing how extraneous solutions may A2.AREI2 Solve simple radical equations in one variable
arise
A2.AREI2 Give examples showing how extraneous solutions may
arise in rational and radical equations
A.AREI3 Solve linear equations and inequalities in one variable,
T3.A.AREI3 Solve simple exponential equations that rely only on the
including equations with coefficients represented by letters
application of the laws of exponents
A2.AREI11 Explain why the x-coordinates of the points where the
graphs of the equations y = f(x) and y = g(x) intersect are the
solutions of the equation f(x) = g(x); find the solutions approximately,
e.g., using technology to graph the functions, make tables of values,
or find successive approximations Include cases where f(x) and/or
g(x) are linear, polynomial, rational, absolute value, exponential, and
logarithmic functions
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T3.A2.AREI11 Define the properties of graphs including linear,
polynomial, rational, absolute value, exponential, and logarithmic
functions
A2.AREI11 Explain why the x-coordinates of the points where the
graphs of the equations y = f(x) and y = g(x) intersect are the
solutions of the equation f(x) = g(x); Including cases where f(x)
and/or g(x) are linear, polynomial, rational, absolute value,
exponential, and logarithmic functions
Resources
Core
Connections
Algebra 2, 2012,
College
Preparatory
Mathematics
(CPM)
Content
Reasoning with
Equations and
Equalities
(cont'd)
Cluster Standard
Represent and solve
equations and inequalities
graphically (cont'd)
Standard
Skill Statements
A2.AREI11 Find the solutions approximately, using technology to
graph the functions, make tables of values, or find successive
approximations Include cases where f(x) and/or g(x) are linear,
polynomial, rational, absolute value, exponential, and logarithmic
functions
Interpreting
Functions
Interpret functions that arise A2.FIF4 For a function that models a relationship between two
in applications in terms of a quantities, interpret key features of graphs and tables in terms of the
context
quantities, and sketch graphs showing key features given a verbal
description of the relationship Key features include: intercepts;
intervals where the function is increasing, decreasing, positive, or
negative; relative maximums and minimums; symmetries; end
behavior; and periodicity
A2.FIF4 Interpret key features of graphs and tables in terms of the
quantities for a function that models a relationship between two
quantities
A2.FIF4 Sketch graphs showing key features given a verbal and
written description of the relationship between two quantities
A2.FIF5 Relate the domain of a function to its graph and, where
A2.FIF5 Make connections between the domain of a function and its
applicable, to the quantitative relationship it describes For example, graph and describe any quantitative relationship
if the function h(n) gives the number of person-hours it takes to
assemble n engines in a factory, then the positive integers would be
an appropriate domain for the function
A2.FIF6 Calculate and interpret the average rate of change of a
function (presented symbolically or as a table) over a specified
interval Estimate the rate of change from a graph
Analyze functions using
different representations
A2.FIF6 Calculate the average rate of change of a function
(presented symbolically or as a table) over a specified interval
A2.FIF6 Interpret the average rate of change of a function
(presented symbolically or as a table) over a specified interval
A2.FIF6 Estimate the rate of change from a graph
A2.FIF7 Graph functions expressed symbolically and show key
A2.FIF7 Graph functions expressed symbolically and show key
features of the graph, by hand in simple cases and using technology features of the graph, by hand in simple cases and using technology
for more complicated cases
for more complicated cases
A2.FIF7 Graph quadratic functions expressed symbolically and show
key features of the graph, by hand in simple cases and using
technology for more complicated cases
A2.FIF7b Graph square root, cube root, and piecewise-defined
A2.FIF7b Graph square root function and show key features of the
functions, including step functions and absolute value functions
graph, by hand in simple cases and using technology for more
complicated cases
A2.FIF7b Graph cube root function and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases
A2.FIF7b Graph piecewise-defined functions, including step
functions and absolute value functions and show key features of the
graph, by hand in simple cases and using technology for more
complicated cases
A2.FIF7c Graph polynomial functions, identifying zeros when
suitable factorizations are available, and showing end behavior
Interpret functions that arise A.FIF7e Graph exponential and logarithmic functions, showing
in applications in terms of a intercepts and end behavior, and trigonometric functions, showing
context
period, midline, and amplitude
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A2.FIF7c Graph polynomial functions
A2.FIF7c Identifying zeros when suitable factorizations are available
A2.FIF7c Graph and describe end behavior
T3.A.FIF7e Graph exponential functions, showing intercepts and
end behavior
A2.FIF7e Graph exponential functions, showing intercepts and end
behavior and show key features of the graph, by hand in simple
cases and using technology for more complicated cases
Resources
Core
Connections
Algebra 2, 2012,
College
Preparatory
Mathematics
(CPM)
Content
Interpreting
Functions
(cont'd)
Building
Functions
Cluster Standard
Interpret functions that arise
in applications in terms of a
context (cont'd)
Skill Statements
A2.FIF7e Graph logarithmic functions, showing intercepts and end
behavior, and show key features of the graph, by hand in simple
cases and using technology for more complicated cases
A2.FIF7e Graph trigonometric functions, showing period, midline,
and amplitude and show key features of the graph, by hand in
simple cases and using technology for more complicated cases
A2.FIF8 Write a function defined by an expression in different but
T3.A2.FIF8 Extend knowledge of factoring patterns to more complex
equivalent forms to reveal and explain different properties of the
cases
function
A2.FIF8 Write a function defined by an expression in different but
equivalent forms
A2.FIF8 Explain different properties of functions
A.FIF9 Compare properties of two functions each represented in a
T3.A.FIF9 Compare properties of two exponential functions each
different way (algebraically, graphically, numerically in tables, or by represented in a different way (algebraically, graphically, numerically
verbal descriptions). For example, given a graph of one quadratic
in tables, or by verbal descriptions)
function and an algebraic expression for another, say which has the A2.FIF9 Compare properties of two functions each represented in a
larger maximum.
different way (algebraically, graphically, numerically in tables, or by
verbal descriptions)
Build a function that models A.FBF1 Write a function that describes a relationship between two
T3.A.FBF1 Write a function that describes an exponential
a relationship between two quantities
relationship between two quantities
quantities
A2.FBF1 Write a function that describes a relationship between two
quantities
A2.FBF1b Combine standard function types using arithmetic
T3.A2.FBF1b Identify and solve exponential functions
operations For example, build a function that models the
A2.FBF1b Combine standard function types using arithmetic
temperature of a cooling body by adding a constant function to a
operations
decaying exponential, and relate these functions to the model
Build new functions from
existing functions
Standard
A.FBF3 Identify the effect on the graph of replacing f(x) by f(x) + k, k
f(x), f(kx), and f(x + k) for specific values of k (both positive and
negative); find the value of k given the graphs Experiment with
cases and illustrate an explanation of the effects on the graph using
technology Include recognizing even and odd functions from their
graphs and algebraic expressions for them
T3.A.FBF3 Find the value of k given a graph of an exponential
function
A2.FBF3 Experiment with cases using technology and illustrate an
explanation of the effects on the graph to identify the effect on the
graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific
values of k (both positive and negative)
A2.FBF3 Find the value of k given a graph
A2.FBF3 Recognize even and odd functions from their graphs and
algebraic expressions for them
A2.FBF4 Find inverse functions a Solve an equation of the form f(x) A2.FBF4 Find the inverse of simple functions including, but not
= c for a simple function f that has an inverse and write an
limited to, linear, quadratic, rational, radical and exponential
expression for the inverse For example, f(x) = 2 x3 or f(x) = (x+1)/(x1) for x ≠ 1
Linear,
Quadratic, and
Exponential
Models
Construct and compare
linear, quadratic, and
exponential models and
solve problems
A.FLE1 Distinguish between situations that can be modeled with
linear functions and with exponential functions
A.FLE1a Prove that linear functions grow by equal differences over
equal intervals; and that exponential functions grow by equal factors
over equal intervals
A.FLE1c Recognize situations in which a quantity grows or decays
by a constant percent rate per unit interval relative to another
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T3.A.FLE1 Distinguish between situations that can be modeled with
linear functions and with exponential functions
T3.A.FLE,1a Prove that exponential functions grow by equal factors
over equal intervals
T3.A.FLE1c Recognize situations in which a quantity grows or
decays by a constant percent rate per unit interval relative to another
Resources
Core
Connections
Algebra 2, 2012,
College
Preparatory
Mathematics
(CPM)
Content
Linear,
Quadratic, and
Exponential
Models (cont'd)
Cluster Standard
Construct and compare
linear, quadratic, and
exponential models and
solve problems (cont'd)
Standard
A.FLE2 Construct linear and exponential functions, including
arithmetic and geometric sequences, given a graph, a description of
a relationship, or two input-output pairs (include reading these from
a table)
FLE3 Observe using graphs and tables that a quantity increasing
exponentially eventually exceeds a quantity increasing linearly,
quadratic ally, or (more generally) as a polynomial function
Skill Statements
T3.A.FLE2 Construct exponential functions, including arithmetic
sequences, given a graph
T3.A.FLE2 Construct exponential functions, including arithmetic
sequences, given a description of a relationship
T3.A.FLE2 Construct exponential functions, including arithmetic
sequences, given a two input-output pair
T3.A.FLE3 Observe using graphs and tables that a quantity
increasing exponentially eventually exceeds a quantity increasing
linearly
A2.FLE4 For exponential models, express as a logarithm the
T3.A2.FLE4 Identify the properties of exponential functions
solution to a bct = d where a, c, and d are numbers and the base b is A2.FLE4 Rewrite exponential models in the form a*b^(ct) = d where
2, 10, or e; evaluate the logarithm using technology
a, c, and d are numbers, and the base b is 2, 10, or e, as a logarithm
Trigonometric
Functions
Interpret expressions for
functions in terms of the
situation they model
Extend the domain of
trigonometric functions
using the unit circle
A2.FLE4 Evaluate the logarithm using technology
A.FLE5 Interpret the parameters in a linear or exponential function in T3.A.FLE5 Interpret the parameters in an exponential function in
terms of a context
terms of a context
A2.FTF1 Understand radian measure of an angle as the length of
the arc on the unit circle subtended by the angle
A2.FTF1 Define radian measure of an angle as the length of the arc
on the unit circle subtended by the angle
A2.FTF2 Explain how the unit circle in the coordinate plane enables
the extension of trigonometric functions to all real numbers,
interpreted as radian measures of angles traversed
counterclockwise around the unit circle
A2.FTF2 Explain how the unit circle in the coordinate plane extends
trigonometric functions to angles greater than 2 pi radians or 360
degrees and less than 0 degree/radians
A2.FTF2 Recognize that angle measures, in either radian or
degrees, that are traversed counterclockwise around the unit circle
are positive angles and those traversed clockwise around the unit
circle are negative angles
Model periodic phenomena A2.FTF5 Choose trigonometric functions to model periodic
with trigonometric functions phenomena with specified amplitude, frequency, and midline
A2.FTF5 Choose trigonometric functions (sine, cosine or tangent) to
model periodic phenomena with specified amplitude, frequency, and
midline
A2.FTF8 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1
A2.FTF8 Use the Pythagorean identity to find sin (θ), cos (θ), or tan
(θ), given sin (θ), cos (θ), or tan (θ), and the quadrant of the angle
Prove and apply
trigonometric identities
A2.FTF8 Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and
use it to find sin (θ), cos (θ), or tan (θ), given sin (θ), cos (θ), or tan
(θ), and the quadrant of the angle
Interpreting
Categorical and
Quantitative
Data
Summarize, represent, and
interpret data on a single
count or measurement
variable
A2.SID4 Use the mean and standard deviation of a data set to fit it
to a normal distribution and to estimate population percentages
Recognize that there are data sets for which such a procedure is not
appropriate Use calculators, spreadsheets, and tables to estimate
areas under the normal curve
Making
Inferences and
Justifying
Conclusions
Understand and evaluate
random processes
underlying statistical
experiments
A2.SIC1 Understand statistics as a process for making inferences
about population parameters based on a random sample from that
population
A2.SIC2 Decide if a specified model is consistent with results from a A2.SIC2 Decide if a specified model is consistent with results from a
given data-generating process, e.g., using simulation For example, a given data-generating process, e.g., using simulation
model says a spinning coin falls heads up with probability 05 Would
a result of 5 tails in a row cause you to question the model?
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A2.SID4 Estimate population percentages using the mean and
standard deviation of a data set to fit it to a normal distribution
A2.SID4 Recognize that there are data sets for which such a
procedure is not appropriate
A2.SID4 Estimate areas under the normal curve using calculators,
spreadsheets, and tables
A2.SIC1 Make inferences about population parameters based on a
random sample from that population using statistics
Resources
Core
Connections
Algebra 2, 2012,
College
Preparatory
Mathematics
(CPM)
Content
Making
Inferences and
Justifying
Conclusions
(cont'd)
Cluster Standard
Standard
Make inferences and justify A2.SIC3 Recognize the purposes of and differences among sample
conclusions from sample
surveys, experiments, and observational studies; explain how
surveys, experiments and
randomization relates to each
observational studies
A2.SIC4 Use data from a sample survey to estimate a population
mean or proportion; develop a margin of error through the use of
simulation models for random sampling
Using Probability Use probability to evaluate
to Make
outcomes of decisions
Decisions
Fluency
Interpret the structure of
expressions
Conditional
Probability and
the Rules of
Probability
Understand independence
and conditional probability
and use them to interpret
data
Skill Statements
A2.SIC3 Recognize the purposes of and differences among sample
surveys, experiments, and observational studies
A2.SIC3 Explain how randomization relates to sample surveys,
experiments, and observational studies
Resources
Core
Connections
Algebra 2, 2012,
College
Preparatory
A2.SIC4 Estimate a population mean or proportion using data from a Mathematics
(CPM)
sample survey
A2.SIC4 Develop a margin of error through the use of simulation
models for random sampling
A2.SIC5 Use data from a randomized experiment to compare two
A2.SIC5 Compare two treatments using data from a randomized
treatments; use simulations to decide if differences between
experiment
parameters are significant
A2.SIC5 Decide if differences between parameters are significant
using simulations
A2.SIC6 Evaluate reports based on data
A2.SIC6 Evaluate reports based on data
A2.SMD6 (+) Use probabilities to make fair decisions (e.g., drawing A2.SMD6 (+) Make fair decisions using probabilities (e.g., drawing
by lots, using a random number generator)
by lots, using a random number generator)
A2.SMD7 (+) Analyze decisions and strategies using probability
A2.SMD7 (+) Analyze decisions and strategies using probability
concepts (e.g., product testing, medical testing, pulling a hockey
concepts (e.g., product testing, medical testing, pulling a hockey
goalie at the end of a game)
goalie at the end of a game)
A2.ASSE2 Use the structure of an expression to identify ways to
A2.ASSE2 Recognize the structure of an expression and identify
rewrite it For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing ways in order to rewrite the expression in equivalent forms
it as a difference of squares that can be factored as (x2 – y2)(x2 +
y2)
G.SCP1 Describe events as subsets of a sample space (the set of T1.G.SCP1 Describe events as subsets of a sample space (the set
outcomes) using characteristics (or categories) of the outcomes, or of outcomes) using characteristics (or categories) of the outcomes
as unions, intersections, or complements of other events (“or,” “and,”
“not”)
T1.G.SCP1 Describe events as subsets of a sample space (the set
of outcomes) using unions, intersections, or complements of other
events (“or,” “and,” “not”)
G.SCP2 Understand that two events A and B are independent if the T1.G.SCP2 Recognize that the probability of two independent
probability of A and B occurring together is the product of their
events A and B occurring together is the product of their probabilities
probabilities, and use this characterization to determine if they are
independent
T1.G.SCP2 Recognize if the probability of events A and B occurring
together is the product of their probabilities, then events A and B are
independent
G.SCP3 Understand the conditional probability of A given B as P(A T1.G.SCP3 Recognize the conditional probability of A given B as
and B)/P(B), and interpret independence of A and B as saying that P(A and B)/P(B)
the conditional probability of A given B is the same as the probability T1.G.SCP3 Interpret independence of A and B as saying that the
of A, and the conditional probability of B given A is the same as the conditional probability of A given B is the same as the probability of
probability of B
A, and the conditional probability of B given A is the same as the
probability of B
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Content
Conditional
Probability and
the Rules of
Probability
(cont'd)
Cluster Standard
Understand independence
and conditional probability
and use them to interpret
data (cont'd)
Use the rules of probability
to compute probabilities of
compound events in a
uniform probability model
Literacy of Math Craft and Structure
Integration of Knowledge
and Ideas
Text Type and Purposes
Standard
G.SCP4 Construct and interpret two-way frequency tables of data
when two categories are associated with each object being
classified. Use the two-way table as a sample space to decide if
events are independent and to approximate conditional probabilities.
For example, collect data from a random sample of students in your
school on their favorite subject among math, science, and English.
Estimate the probability that a randomly selected student from your
school will favor science given that the student is in tenth grade. Do
the same for other subjects and compare the results
Skill Statements
T1.G.SCP4 Construct and interpret two-way frequency tables of data
when two categories are associated with each object being
classified
T1.G.SCP4 Determine if events are independent by using a twoway table as a sample space to approximate conditional probabilities
G.SCP5 Recognize and explain the concepts of conditional
probability and independence in everyday language and everyday
situations. For example, compare the chance of having lung cancer
if you are a smoker with the chance of being a smoker if you have
lung cancer
T1.G.SCP5 Recognize the concepts of conditional probability and
independence in everyday language and everyday situations
T1.G.SCP5 Explain the concepts of conditional probability and
independence in everyday language and everyday situations
G.SCP6 Find the conditional probability of A given B as the fraction
of B’s outcomes that also belong to A, and interpret the answer in
terms of the model
T1.G.SCP6 Calculate the conditional probability of A given B as the
fraction of B’s outcomes that also belong to A
T1.G.SCP6 Interpret the conditional probability in terms of the model
G.SCP7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and T1.G.SCP7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A
B), and interpret the answer in terms of the model
and B)
T1.G.SCP7 Interpret the Addition Rule in terms of the model
RST4 Interpret words and phrases as they are used in a text,
11/12.RST4 Determine the meaning of symbols, key terms, and
including determining technical, connotative, and figurative
other domain-specific words and phrases as they are used in a
meanings, and analyze how specific word choices shape meaning or specific scientific or technical context
tone
RST7 Integrate and evaluate content presented in diverse media
11/12.RST7 Integrate and evaluate multiple sources of information
and formats, including visually and quantitatively, as well as in words presented in diverse formats and media (e.g., quantitative data,
video, multimedia) in order to address a question or solve a problem
WHST2 Write informative/explanatory texts to examine and convey
complex ideas and information clearly and accurately through the
effective selection, organization, and analysis of content
11/12.WHST2 Write informative/explanatory texts, including the
narration of historical events, scientific procedures/ experiments, or
technical processes
11/12.WHST2a Introduce a topic and organize complex ideas,
concepts, and information so that each new element builds on that
which precedes it to create a unified whole; include formatting (e.g.,
headings), graphics (e.g., figures, tables), and multimedia when
useful to aiding comprehension
11/12.WHST2b Develop the topic thoroughly by selecting the most
significant and relevant facts, extended definitions, concrete details,
quotations, or other information and examples appropriate to the
audience’s knowledge of the topic
11/12.WHST2c Use varied transitions and sentence structures to
link the major sections of the text, create cohesion, and clarify the
relationships among complex ideas and concepts
11/12.WHST2d Use precise language, domain-specific vocabulary
and techniques such as metaphor, simile, and analogy to manage
the complexity of the topic; convey a knowledgeable stance in a
style that responds to the discipline and context as well as to the
expertise of likely readers
8 of 9
Resources
Core
Connections
Algebra 2, 2012,
College
Preparatory
Mathematics
(CPM)
Content
Cluster Standard
Literacy of Math Text Type and Purposes
(cont'd)
(cont'd)
Standard
Skill Statements
11/12.WHST2e Provide a concluding statement or section
that follows from and supports the information or explanation
provided (e.g., articulating implications or the significance of the
topic)
Mathematical
Practices
MP1 Make sense of problems and persevere in solving them
MP2 Reason abstractly and quantitatively
MP3 Construct viable arguments and critique the reasoning of
others
MP4 Model with mathematics
MP5 Use appropriate tools strategically
MP6 Attend to precision
MP7 Look for and make use of structure
MP8 Look for and express regularity in repeated reasoning
9 of 9
Resources
Core
Connections
Algebra 2, 2012,
College
Preparatory
Mathematics
(CPM)